editing disabled

The temperaments listed are 29edo-distinct, meaning that they are all different even if tuned in 29edo. The ordering is by increasing complexity of 3. The temperament of lowest TE complexity supported by the patent val was chosen as the representative for each class of edo-distinctness.


5-limit temperaments

Period generator
Wedgie
Name
Complexity
Commas
29 12
<<1 -8 -15]]
Helmholtz
3.103
32805/32768
29 6
<<2 13 16]]
Immunity
4.157
1638400/1594323
29 4
<<3 5 1]]
Porcupine
1.663
250/243
29 3
<<4 -3 -14]]
Negri
2.739
16875/16384
29 14
<<5 18 17]]

5.519
409600000/387420489
29 2
<<6 -19 -44]]

8.646
18160335421875/17592186044416
29 10
<<7 2 -13]]

3.303
78125/73728
29 13
<<8 23 18]]

7.012
102400000000/94143178827
29 11
<<9 -14 -43]]

8.269
9341736328125/8796093022208
29 7
<<10 7 -12]]

4.455
9765625/8957952
29 9
<<11 -1 -27]]

5.836
146484375/134217728
29 1
<<17 9 -25]]

7.664
762939453125/660451885056
29 8
<<13 12 -11]]

5.857
1220703125/1088391168
29 5
<<15 -4 -41]]

8.498
2471923828125/2199023255552

7-limit temperaments

Period generator
Wedgie
Name
Complexity
Commas
29 12
<<1 -8 -14 -15 -25 -10]]
Garibaldi
3.823
225/224 3125/3087
29 6
<<2 13 1 16 -4 -34]]
Immunity
3.651
49/48 2240/2187
29 4
<<3 5 16 1 17 23]]
Porky
3.362
225/224 250/243
29 3
<<4 -3 2 -14 -8 13]]
Negri
2.245
49/48 225/224
29 14
<<5 18 17 17 13 -11]]

4.821
686/675 2240/2187
29 2
<<6 10 3 2 -12 -21]]
Nautilus
2.943
49/48 250/243
29 10
<<7 2 18 -13 9 36]]

4.251
225/224 6125/5832
29 13
<<8 23 4 18 -16 -55]]

6.241
49/48 560000/531441
29 11
<<9 15 19 3 5 2]]
Ammonite
4.506
250/243 686/675
29 7
<<10 7 5 -12 -20 -8]]

3.751
49/48 3125/3024
29 9
<<11 -1 20 -27 1 49]]

5.909
225/224 84035/78732
29 1
<<17 9 23 -25 -11 28]]

6.682
686/675 21875/20736
29 8
<<13 12 21 -11 -3 15]]

5.238
686/675 3125/3024
29 5
<<14 4 7 -26 -28 5]]

5.436
49/48 78125/73728

11-limit temperaments

Period generator
Wedgie
Name
Complexity
Commas
29 12
<<1 -8 -14 -18 -15 -25 -32 -10 -14 -2]]
Cassandra
3.897
100/99 225/224 245/242
29 6
<<2 13 1 -7 16 -4 -18 -34 -61 -23]]
Immunity
3.977
49/48 55/54 896/891
29 4
<<3 5 16 4 1 17 -4 23 -8 -44]]
Porky
3.020
55/54 100/99 225/224
29 3
<<4 -3 2 15 -14 -8 10 13 45 35]]
Negroni
3.110
49/48 55/54 225/224
29 14
<<5 -11 -12 -3 -29 -33 -22 3 31 33]]
Tritonic
4.596
121/120 225/224 441/440
29 2
<<6 10 3 8 2 -12 -8 -21 -16 12]]
Nautilus
2.548
49/48 55/54 245/242
29 10
<<7 2 18 19 -13 9 6 36 37 -9]]

4.023
55/54 225/224 245/242
29 13
<<8 -6 4 1 -28 -16 -26 26 23 -11]]
Wilsec
3.911
49/48 121/120 225/224
29 11
<<9 15 19 12 3 5 -12 2 -24 -32]]
Ammonite
3.980
55/54 100/99 686/675
29 7
<<10 7 5 23 -12 -20 2 -8 29 47]]

4.064
49/48 55/54 625/616
29 9
<<11 -1 20 5 -27 1 -30 49 15 -55]]

5.264
121/120 225/224 1225/1188
29 1
<<17 9 23 13 -25 -11 -38 28 -1 -43]]

5.913
121/120 625/616 686/675
29 8
<<13 12 21 27 -11 -3 -2 15 21 3]]

4.823
55/54 245/242 625/616
29 5
<<14 4 7 9 -26 -28 -34 5 7 1]]

4.725
49/48 121/120 625/616

13-limit temperaments

Period generator
Wedgie
Name
Complexity
Commas
29 12
<<1 -8 -14 -18 -21 -15 -25 -32 -37 -10 -14 -19 -2 -7 -6]]
Cassandra
3.911
100/99 105/104 196/195 245/242
29 6
<<2 13 1 22 16 16 -4 28 18 -34 6 -11 58 41 -26]]
Impunity
3.934
49/48 91/90 100/99 352/351
29 4
<<3 5 16 4 -5 1 17 -4 -19 23 -8 -30 -44 -73 -32]]
Porky
3.380
55/54 65/64 91/90 100/99
29 3
<<4 -3 2 15 3 -14 -8 10 -10 13 45 18 35 1 -45]]
Negroni
2.793
49/48 55/54 65/64 91/90
29 14
<<5 18 17 26 11 17 13 24 -1 -11 -2 -41 14 -32 -58]]

4.312
91/90 100/99 169/168 245/242
29 2
<<6 10 3 8 19 2 -12 -8 8 -21 -16 7 12 42 36]]
Nautilus
2.806
49/48 55/54 91/90 100/99
29 10
<<7 2 -11 -10 -2 -13 -37 -40 -29 -31 -30 -12 10 35 30]]
Roman
4.163
65/64 100/99 105/104 245/242
29 13
<<8 -6 4 1 6 -28 -16 -26 -20 26 23 36 -11 2 17]]
Wilsec
3.527
49/48 65/64 91/90 121/120
29 11
<<9 15 19 12 14 3 5 -12 -11 2 -24 -23 -32 -31 4]]
Ammonite
3.582
55/54 91/90 100/99 169/168
29 7
<<10 7 5 23 22 -12 -20 2 -2 -8 29 25 47 43 -9]]

3.888
49/48 55/54 91/90 847/845
29 9
<<11 -1 -9 5 1 -27 -45 -30 -39 -18 15 6 45 36 -15]]

4.743
65/64 121/120 169/168 275/273
29 1
<<12 20 6 16 9 4 -24 -16 -30 -42 -32 -53 24 3 -28]]

4.724
49/48 55/54 245/242 343/338
29 8
<<13 12 21 27 17 -11 -3 -2 -21 15 21 -5 3 -30 -41]]

4.362
55/54 91/90 169/168 245/242
29 5
<<14 4 7 9 25 -26 -28 -34 -12 5 7 43 1 44 53]]

4.713
49/48 91/90 121/120 625/616